# Intersection of Sets

Pronunciation: /ˌɪn.tərˈsɛk.ʃən ʌv sɛtz/ Explain

 Figure 1: Intersection. Click on the image to see a representation of A ∩ B.

An intersection of two or more sets is a set containing the members that are in all of the sets. This is spoken, "Set C is the intersection of sets A and B." This is written, C = AB.

#### Properties of Intersection of Sets

PropertyMath StatementDescription
Commutative AB = BA The intersection of sets is commutative
Associative (DE) ∩ F = D ∩ (EF) The intersection of sets is associative
Distributive (DE) ∪ F = (DF) ∩ (EF)
(DE) ∩ F = (DF) ∪ (EF)
The intersection and union of sets are distributive
Table 1: Properties of the intersection of two sets.

### References

1. McAdams, David E.. All Math Words Dictionary, intersection. 2nd Classroom edition 20150108-4799968. pg 101. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. intersection. merriam-webster.com. Encyclopedia Britannica. Merriam-Webster. Last Accessed 8/7/2018. http://www.merriam-webster.com/dictionary/intersection. Buy the book
3. Von Neumann, John and Morgenstern, Oskar. Theory Of Games And Economic Behavior. 3rd edition. pg 63. www.archive.org. Princeton University Press. 1953. Last Accessed 8/7/2018. http://www.archive.org/stream/theoryofgamesand030098mbp#page/n84/mode/1up. Buy the book
4. Goldrei, D.C.. Classic Set Theory: For Guided Independent Study. pg 4. Chapman & Hall Mathematics. July 1, 1996. Last Accessed 8/7/2018. Buy the book
5. Gilbert, Jimmie; and Gilbert Linda. Elements of Modern Algebra. 6th edition. pg 4. Thomson, Brooks/Cole. 2005. Last Accessed 8/7/2018. Buy the book

• McAdams, David E.. Sets. lifeisastoryproblem.com. Life is a Story Problem LLC. 3/12/2009. http://www.lifeisastoryproblem.com/algebra/sets.html.

McAdams, David E. Intersection of Sets. 4/23/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/i/intersection.html.

### Revision History

4/23/2019: Updated equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)